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Showing 1 to 20 of 51 for “"eigenfunction"”.
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Numerical solution of differential equations through empirical eigenfunction expansions
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1995.
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Eigenfunction expansion of the time and space-dependent neutron survival probability equation
… probability is well-approximated by the first eigenfunction of the linear portion of the equation. Not only is strong agreement observed with the semi-analytical solution, extension to other geometries is made accessible and the impact that varying geometry has on the survival probability is …
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Microseismic guided wave eigenfunction theory with application to event depth classification in the Eagle Ford shale
… deep low-velocity zones are investigated using eigenfunction theory, and a novel application for microseismic event depth constraint to an unconventional reservoir is developed. Eigenfunctions, historically used in the analysis of Rayleigh and Love surface waves, allow rapid calculation of …
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Convergence Properties of the Eigenfunction Expansion of the Biharmonic Equation on Rectangular and Semi-Infinite Strips
We consider the problem (DELTA)('2)(w(x,y)) = 0, w((+OR-)1,y) = w(,x)((+OR-)1,y) = 0 with boundary conditions w(,xx)(x,0) = f(x) w(,yy)(x,0) = g(x) on the semi-infinite strip -1 (LESSTHEQ) x (LESSTHEQ) 1, 0 < y.
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A Near-Zone to Far-Zone Transformation Process Utilizing a Formulated Eigenfunction Expansion of Spheroidal Wave-Harmonics
… in doing so. Our approach uses a formulated eigenfunction expansion of spheroidal wave-harmonics to develop two distinct, yet closely related, NZ-FZT algorithms for each type of spheroidal transformation surface. The process only requires knowledge of the E-field along the transformation …
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The Asymptotic Development of The Equations of Nuclear Reactor Theory
… of the fundamental unit-cell transport theory eigenfunction and the fundamental cell-homogenized diffusion theory eigenfunction is shown to correspond to the leading asymptotic solution to the transport equation for large near-critical heterogeneous systems comprised of periodic or …
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Linear mixed effects models in functional data analysis
… the functional predictor using basis function or eigenfunction expansions. In the expansion, the coefficient vector can either be fixed or random. The random coefficient vector is also known as random effects and thus the regression models are in a mixed effects framework. The random effects …
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Variational Methods for p-Laplacian Sturm-Liouville Problems
… of the first eigencurve and its corresponding eigenfunction. In chapters 4 and 5, the nonhomogeneous case is considered. Chapter 4 proves the existence of solutions in the case below the first eigencurve. In Chapter 5 we prove the existence of solutions for the resonant case under two different …
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Diagonalization of 1-D Schrodinger Operators with Piecewise Constant Potentials
… practical. The method used here will apply an eigenfunction expansion technique used in previous research that eliminates the current time-stepping problems.</p>
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Eigenfunctions in chaotic quantum systems
… In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of …
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Finite Element Analysis of Multilayer Transmission Lines and Circuit Components
… used to truncate the simulation domain, and the eigenfunction expansion method is used to connect the circuit component to signal inputs and outputs. A new E-H type eigenfunction expansion formulation is used for inhomogeneous port boundary conditions. Various types of planar structures are …
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Laminar flow with an axially varying heat transfer coefficient
… boundary condition parameter, a variable eigenfunction approach is developed. An analysis is carried out for a periodic heat transfer coefficient, which serves as a model for heat transfer from a duct fitted with an array of evenly spaced fins. Three solution methods for the variable …
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A Simplified Model of Planetary Chemical Vapor Deposition Reactors
… to derive the reactor modeling equation, and the eigenfunction expansion solution is subsequently computed using a previously developed MATLAB object-oriented computational framework. The simulation result for the deposition profile is improved by modifying the inlet boundary condition, and is …
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Theory and applications of chirality in microstrip antennas
… lossless dielectric half-space. An eigenvalue-eigenfunction approach, specifically the Ohm-Raleigh method, is employed to obtain a modal expression for the full-wave Green's function. By using asymptotic techniques, the far-field electric field is found for an elemental point dipole source. The …
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Oscillations and waves in anisotropic plasmas
… solutions are put into the form of a generalized eigenfunction expansion with eigenmodes corresponding to zeros of the appropriate plasma dispersion function. The expansion coefficients for eigenmodes corresponding to simple and second order real zeros of the plasma dispersion function are also …
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Equilibrium Measures for Symbolic Spaces Using Dimension Theory
… finite type, we construct the eigenmeasure and eigenfunction that appear in the Ruelle-Peron-Frobenius theorem using this dimension theoretic machinery.
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Minimum-weight design of compressively loaded stiffened panels for postbuckling response
… analysis code, NLPAN, which requires buckling eigenfunction information from the buckling analysis code, VIPASA, is linked with the optimization code ADS. A blade-stiffened and T-stiffened panel are designed for specified loads using NLPANOPT for postbuckling response and PASCO for …
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A functional analytic approach to multigroup transport theory
… and invertible transfer matrix. The Case-type eigenfunction expansion formulas for the solutions of these problems are explicitly obtained. For the half-space case, the formulas are expressed in terms of two matrices X and Y which provide the Wiener-Hopf factorization of the dispersion matrix. …
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Finite Element Analysis Of Left-handed Waveguides
… also analyzed using finite element method with eigenfunction expansion technique.
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Plastic buckling of initially imperfect stiffened cylinders in axial compression
… being the critical compressive load and the eigenfunction being the corresponding buckling mode. Results are presented or shells of different geometries and material properties, a limited comparison of theoretical results as obtained by this analysis with available experimental data is also …
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